Question

The width of a rectangle is 4 units shorter than three-fourths the length; x. Write an expression that represents the perimeter of the rectangle.

Answer 1

The expression that represents the perimeter of the rectangle is 4x² + 14x - 3 = 0

How to determine the expression

The formula for perimeter of a rectangle is given as;

Perimeter = 2 ( length + width)

Let the length of the rectangle be x

Width of the rectangle be y

From the information given, we have that;

y = 4 - 3/4x

Make into linear equation

y = 16x - 3 / 4x

Now, let's substitute the variables into the formula

Perimeter = 2 ($\frac{16x -3 }{4x} + x$)

Find the LCM of the bracket

Perimeter = $2(\frac{16x - 3 + 4x^2}{4x} )$

Perimeter = $\frac{4x^2 + 16x - 3}{2x}$

2x = 4x² + 16x - 3

Collect like terms

4x² + 16x - 2x - 3 = 0

4x² + 14x - 3 = 0

Thus, the expression that represents the perimeter of the rectangle is 4x² + 14x - 3 = 0

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